A Probabilistic Distance-Based Modeling and Analysis for Cellular Networks With Underlaying Device-to-Device Communications

Tong, Fei; Wan, Ying; Zheng, Lei; Pan, Jianping; Cai, Lin

doi:10.1109/twc.2016.2625301

Cited by 23 publications

(13 citation statements)

References 24 publications

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“…We consider that

scriptS

and

scriptU

are deployed stochastically uniformly within a circle of radius R with attacker

scriptA

at its centre. The proposed configuration represents a practical ad‐hoc network scenario where nodes can be placed randomly in the deployment region [16], and an attacker invades the network with a malicious intention of eavesdropping or jamming. The centre location of

scriptA

will offer leverage to it the maximal possible attacking capability.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…As noted in the literature survey, PLS in spatial stochastic networks is mainly studied under the assumption of homogeneous PPP based deployment of nodes [12]- [15], [24] which are non-viable in several practical scenarios [17], [18]. Moreover, most studies of stochastic networks consider a passive attacker that can only eavesdrop.…”

Section: B Research Gap and Motivationmentioning

confidence: 99%

“…Furthermore, it is incapable of analysing the average performance measures at a randomly deployed node, which has significant importance in realistic networks. Some scenarios showing limitations of the above models under device‐to‐device (D2D) or sensor networks have been examined in [15, 16].…”

Section: Introductionmentioning

confidence: 99%

“…In [21], the secrecy performance of a wireless network with randomly deployed hybrid attackers is analysed using stochastic geometry tools and random matrix theory. Recently, much attention is being paid to the utilisation of distance distributions as a complement to PPP models for performance analysis in wireless networks [15, 16] without considering secrecy requirements.…”

Section: Introductionmentioning

confidence: 99%

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QoS‐aware stochastic spatial PLS model for analysing secrecy performance under eavesdropping and jamming

2020

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Securing wireless communication, being inherently vulnerable to eavesdropping and jamming attacks, becomes more challenging in resource-constrained networks like Internet-of-Things. Towards this, physical layer security (PLS) has gained significant attention due to its low complexity. In this paper, we address the issue of random inter-node distances in secrecy analysis and develop a comprehensive quality-of-service (QoS) aware PLS framework for the analysis of both eavesdropping and jamming capabilities of attacker. The proposed solution covers spatially stochastic deployment of legitimate nodes and attacker. We characterise the secrecy outage performance against both attacks using inter-node distance based probabilistic distribution functions. The model takes into account the practical limits arising out of underlying QoS requirements, which include the maximum distance between legitimate users driven by transmit power and receiver sensitivity. A novel concept of eavesdropping zone is introduced, and relative impact of jamming power is investigated. Closed-form expressions for asymptotic secrecy outage probability are derived offering insights into design of optimal system parameters for desired security level against the attacker's capability of both attacks. Analytical framework, validated by numerical results, establishes that the proposed solution offers potentially accurate characterisation of the PLS performance and key design perspective from point-of-view of both legitimate user and attacker.

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“…We consider that

scriptS

and

scriptU

are deployed stochastically uniformly within a circle of radius R with attacker

scriptA

scriptA

will offer leverage to it the maximal possible attacking capability.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: B Research Gap and Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

QoS‐aware stochastic spatial PLS model for analysing secrecy performance under eavesdropping and jamming

2020

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“…On the basis of Baltzis, 23 the node-node distance distribution function was calculated in Baltzis. 24 Based on kinematic measure in integral geometry in Santalo, 25 a cellular network with a single subregion was considered and some results of NDDs were given in Tong et al, 26 then a systematic, algorithmic approach was proposed to getting the random-torandom NDDs for arbitrarily-shaped wireless networks, and the NDDs function was usually an implicit formula in Tong and Pan. 27 And the derivation of the closed-form NDDs is a complicated problem in arbitrarily shaped networks.…”

Section: G(ve)mentioning

confidence: 99%

Nodal distance distributions in cluster flight spacecraft network

Shi

et al. 2020

Math Methods in App Sciences

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The high-speed flight of cluster flight spacecraft modules increases the uncertainty of network topology. In order to better design the orbital of the cluster flight spacecraft and improve the performance of cluster flight spacecraft network (CFSN), this paper studies the nodal distance distributions (NDDs). First, based on twin-satellites mode, the mobility model of nodes is established. And then by adopting empirical statistical method and curve fitting method, the solution of the nodal distance density function in the CFSN is obtained. Second, the probability density function is applied to the model distancedependent path loss, and the probability density of path loss under the model is analyzed. Finally, the distributions of maximum and minimum distance among multiple nodes and the threshold range of nodal connection distance are derived, and the probabilistic connectivity matrix of any time slot in the orbital hyper-period and spatial-temporal evolution graphs under different thresholds is obtained. The analytical results verify the feasibility of the model and the approximate solution of the NDDs in this paper. This method also provides a theoretical reference for the nodal connection in irregular wireless networks.

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Distance distribution between two random points in arbitrary polygons

Pure

Durrani

Tong

et al. 2021

Math Methods in App Sciences

Self Cite

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Distance distributions are a key building block in many subfields in mathematics, science and engineering. In this paper, we propose a novel framework for analytically computing the closed form probability density function (PDF) of the distance between two random points each uniformly randomly distributed in respective arbitrary polygon regions. The proposed framework is based on measure theory and uses polar decomposition for simplifying and calculating the integrals to obtain closed form results. We validate our proposed framework by comparison with simulations and published closed form results in the literature for simple cases. We illustrate the versatility and advantage of the proposed framework by deriving closed form results for a case not yet reported in the literature. Finally, we also develop a Mathematica implementation of the proposed framework which allows a user to define any two arbitrary (concave or convex) polygons, with or without holes, which may be disjoint or overlap or coincide and determine the distance distribution numerically.

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A Probabilistic Distance-Based Modeling and Analysis for Cellular Networks With Underlaying Device-to-Device Communications

Cited by 23 publications

References 24 publications

QoS‐aware stochastic spatial PLS model for analysing secrecy performance under eavesdropping and jamming

QoS‐aware stochastic spatial PLS model for analysing secrecy performance under eavesdropping and jamming

Nodal distance distributions in cluster flight spacecraft network

Distance distribution between two random points in arbitrary polygons

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